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Abstract

The light scattering by a spherical particle with radial anisotropic permittivity ε and permeability μ are discussed in detail by expanding Mie theory. With the modified vector potential formulation, the electric anisotropy effects on scattering efficiency are addressed by studying the extinction, scattering, absorption and radar cross sections following the change of the transverse permittivity εt, the longitudinal permittivity εr and the particle size q. The huge scattering cross sections are shown by considering the possible coupling between active medium and plasmon polaritons and this will be possible to result in spaser from the active plasmons of small particle.

Figures (8)

Fig. 1 The maximal value of Qext for each resonance mode as a function of the dissipative damping Im[εD] for the size q = 1 (A) and q = 0.5 (B). The Qext as a function of both frequency ω and Im[εD] for dipole and quadrupole modes of the particle with size q = 1 shown in the inset of (A).

Fig. 2 The maximal value of Qext as a function of Re[εD] with different Im[εD] (A), the maximal or minimal values of Qsca and Qabs as a function of Im[εD] with Re[εD] = −2.2 (B), maximal value of Qext as a function of Im[εr] with different Re[εr] and the ratio εt/εr (C and D).

Fig. 4 Log[Qext] as a function of permittivity εD and size q under the nondissipative limit (Im[εD] = 0) (A), the maximal value of Log[Qext] as a function of Re[εD] and Im[εD] (B), the maximal value of Log[Qsca] as a function of Im[εr] and the ratio |εt|/|εr| for Re[εr] = −2.5 and εt = (−2.5 + iIm[εr])|εt|/|εr|(C), Log[Qsca] as a function of the ratio |εt|/|εr| and size q for εr = −2.5 −0.1i and εt = (−2.5 −0.1i)|εt|/|εr|(D).

Fig. 3 Log[Qmax ext] as a function of both εr and εt/εr (A), Qext as a function of q and εt/εr with fixed longitudinal permittivity εr = −2.5 (B) and Qext as a function of q and εr with fixed ratio εt/εr = 0.75 (C), with the nondissipative limit (Im[εr] = 0 and Im[εt] = 0).

Fig. 6 the maximal value of scattering amplitude |
b1e| as a function of Re[εr] and Re[εt] with fixed Im[εr](= −0.05) and Im[εt](= 0.008) for εr as active medium (A), with fixed Im[εr](= 0.001) and Im[εt](= −0.02) for εt as active medium (B).

Fig. 7 the scattering amplitude
Log[|b1e|] as a function of Re[εr] and q with fixed Im[εr](= −0.05) and Im[εt](= 0.008) (Re[εt] is chosen by the formula Re[εt] = −2.62 + 0.608Re[εr] − 0.110Re[εr]2 + 0.008Re[εr]3)(A), the scattering amplitude
Log[|b1e|] as a function of Re[εr] and q with fixed Im[εr](= 0.001) and Im[εt](= −0.02) (Re[εt] is chosen by the formula Re[εt] = 0.389 – 0.154Re[εr])(B), the maximal value of scattering amplitude
Log[|b1e|] as a function of f(Im[εr]) and Im[εt] with εr = 3 – f(Im[εt])Im[εt] i and Re[εt] = −1.5604 (C) and the maximal value of scattering amplitude
Log[|b1e|] as a function of f(Im[εr]) and Im[εr] with Re[εr] = −12 and εt = 2.237 – f(Im[εr])Im[εr]i (D).

Fig. 8 High scattering efficiencies with huge radar backscattering cross section. Qrbs as the function of size q for εr with the property of energy-gain (A and B) and for εt with the property of energy-gain (C and D).